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Pricing Cryptocurrency Options

Author

Listed:
  • Ai Jun Hou
  • Weining Wang
  • Cathy Y. H. Chen
  • Wolfgang Karl Hardle

Abstract

Cryptocurrencies, especially Bitcoin (BTC), which comprise a new digital asset class, have drawn extraordinary worldwide attention. The characteristics of the cryptocurrency/BTC include a high level of speculation, extreme volatility and price discontinuity. We propose a pricing mechanism based on a stochastic volatility with a correlated jump (SVCJ) model and compare it to a flexible co-jump model by Bandi and Ren\`o (2016). The estimation results of both models confirm the impact of jumps and co-jumps on options obtained via simulation and an analysis of the implied volatility curve. We show that a sizeable proportion of price jumps are significantly and contemporaneously anti-correlated with jumps in volatility. Our study comprises pioneering research on pricing BTC options. We show how the proposed pricing mechanism underlines the importance of jumps in cryptocurrency markets.

Suggested Citation

  • Ai Jun Hou & Weining Wang & Cathy Y. H. Chen & Wolfgang Karl Hardle, 2020. "Pricing Cryptocurrency Options," Papers 2009.11007, arXiv.org.
    • Handle: RePEc:arx:papers:2009.11007
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    References listed on IDEAS

    as
    1. Asgharian, Hossein & Nossman, Marcus, 2011. "Risk contagion among international stock markets," Journal of International Money and Finance, Elsevier, vol. 30(1), pages 22-38, February.
    2. Hossein Asgharian & Christoffer Bengtsson, 2006. "Jump Spillover in International Equity Markets," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 167-203.
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    Cited by:

    1. Konstantin Häusler & Hongyu Xia, 2022. "Indices on cryptocurrencies: an evaluation," Digital Finance, Springer, vol. 4(2), pages 149-167, September.
    2. Boyi Li & Weixuan Xia, 2024. "Crypto Inverse-Power Options and Fractional Stochastic Volatility," Papers 2403.16006, arXiv.org.
    3. Zhang, Chuanhai & Ma, Huan & Liao, Xiaosai, 2023. "Futures trading activity and the jump risk of spot market: Evidence from the bitcoin market," Pacific-Basin Finance Journal, Elsevier, vol. 78(C).
    4. Christian Gourieroux & Joann Jasiak & Michelle Tong, 2021. "Convolution‐based filtering and forecasting: An application to WTI crude oil prices," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(7), pages 1230-1244, November.
    5. Bandi, Federico M. & Renò, Roberto, 2022. "β in the tails," Journal of Econometrics, Elsevier, vol. 227(1), pages 134-150.
    6. Lian, Yu-Min & Chen, Jun-Home, 2021. "Pricing virtual currency-linked derivatives with time-inhomogeneity," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 424-439.
    7. Lin, Min-Bin & Khowaja, Kainat & Chen, Cathy Yi-Hsuan & Härdle, Wolfgang Karl, 2020. "Blockchain mechanism and distributional characteristics of cryptos," IRTG 1792 Discussion Papers 2020-027, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    8. Zhang, Chuanhai & Zhang, Zhengjun & Xu, Mengyu & Peng, Zhe, 2023. "Good and bad self-excitation: Asymmetric self-exciting jumps in Bitcoin returns," Economic Modelling, Elsevier, vol. 119(C).
    9. Burda, Michael C., 2021. "Valuing cryptocurrencies: Three easy pieces," IRTG 1792 Discussion Papers 2021-011, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    10. Xia, Lan & Roggeveen, Anne L., 2022. "How collective stress affects price fairness perceptions: The role of nostalgia," Journal of Business Research, Elsevier, vol. 152(C), pages 361-371.
    11. Matic, Jovanka Lili & Packham, Natalie & Härdle, Wolfgang Karl, 2021. "Hedging Cryptocurrency Options," MPRA Paper 110985, University Library of Munich, Germany.
    12. Konstantin Hausler & Wolfgang Karl Hardle, 2021. "Cryptocurrency Dynamics: Rodeo or Ascot?," Papers 2103.12461, arXiv.org, revised Jan 2022.
    13. Wujun Lv & Tao Pang & Xiaobao Xia & Jingzhou Yan, 2023. "Dynamic portfolio choice with uncertain rare-events risk in stock and cryptocurrency markets," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-28, December.
    14. Huang, Jing-Zhi & Ni, Jun & Xu, Li, 2022. "Leverage effect in cryptocurrency markets," Pacific-Basin Finance Journal, Elsevier, vol. 73(C).
    15. Melanie Cao & Batur Celik, 2021. "Valuation of bitcoin options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(7), pages 1007-1026, July.
    16. Abubakr Naeem, Muhammad & Iqbal, Najaf & Lucey, Brian M. & Karim, Sitara, 2022. "Good versus bad information transmission in the cryptocurrency market: Evidence from high-frequency data," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 81(C).
    17. Elisa Al`os & Eulalia Nualart & Makar Pravosud, 2023. "On the implied volatility of Inverse and Quanto Inverse options under stochastic volatility models," Papers 2401.00539, arXiv.org.
    18. Almeida, José & Gonçalves, Tiago Cruz, 2023. "A systematic literature review of investor behavior in the cryptocurrency markets," Journal of Behavioral and Experimental Finance, Elsevier, vol. 37(C).
    19. Danial Saef & Yuanrong Wang & Tomaso Aste, 2022. "Regime-based Implied Stochastic Volatility Model for Crypto Option Pricing," Papers 2208.12614, arXiv.org, revised Sep 2022.
    20. Jovanka Lili Matic & Natalie Packham & Wolfgang Karl Härdle, 2023. "Hedging cryptocurrency options," Review of Derivatives Research, Springer, vol. 26(1), pages 91-133, April.
    21. José Almeida & Tiago Cruz Gonçalves, 2022. "A Systematic Literature Review of Volatility and Risk Management on Cryptocurrency Investment: A Methodological Point of View," Risks, MDPI, vol. 10(5), pages 1-18, May.
    22. Carol Alexander & Ding Chen & Arben Imeraj, 2021. "Inverse and Quanto Inverse Options in a Black-Scholes World," Papers 2107.12041, arXiv.org, revised Oct 2022.
    23. Häusler, Konstantin & Härdle, Wolfgang, 2021. "Rodeo or ascot: Which hat to wear at the crypto race?," IRTG 1792 Discussion Papers 2021-007, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    24. Kuo-Shing Chen, 2024. "Investigating the Impact of Financial Reporting for Cryptocurrencies on Company Value," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 14(3), pages 1-6.

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    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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